where \(k^{*}\)  is a tuning parameter of the algorithm, whose role
is described in the following. For each trajectory \(n\) , a random
number of copies of the trajectory are generated at time \(t_{i}\) .
The expectation value of the number of copies generated by a trajectory
\(n\) is proportional to its weight \(W_{n}^{i}\) . Trajectories featuring
large values of the time average of the observable will thus produce
many copies of themselves, while trajectories featuring small values
of the observable will not produce any copies and will effectively
be killed. For practical reasons it is convenient to generate the
copies in such a way to fix the total number of trajectories to be
always exactly \(N\)  after each resampling, as described in [1]}.
The value of the parameter \(k^{*}\)  defines how stringent is the selection.
For large values of \(k^{*}\)  only the trajectories with the very largest
values of the observable will be allowed to generate copies of themselves.
If the system is deterministic, like in the case of climate models,
a small random perturbation is added just after the cloning to each
trajectory, so that copies of the same trajectory will evolve differently.
See [1]} for more details.
